Simplify the following expression: $t = \dfrac{-5a^2 + 5a + 150}{a - 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ t =\dfrac{-5(a^2 - 1a - 30)}{a - 6} $ Then we factor the remaining polynomial: $a^2 {-1}a {-30} $ ${-6} + {5} = {-1}$ ${-6} \times {5} = {-30}$ $ (a {-6}) (a + {5}) $ This gives us a factored expression: $\dfrac{-5(a {-6}) (a + {5})}{a - 6}$ We can divide the numerator and denominator by $(a + 6)$ on condition that $a \neq 6$ Therefore $t = -5(a + 5); a \neq 6$